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Properties

Label 1425.2.v
Level $1425$
Weight $2$
Character orbit 1425.v
Rep. character $\chi_{1425}(226,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $378$
Sturm bound $400$

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Defining parameters

Level: \( N \) \(=\) \( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1425.v (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1425, [\chi])\).

Total New Old
Modular forms 1272 378 894
Cusp forms 1128 378 750
Eisenstein series 144 0 144

Trace form

\( 378 q + 6 q^{4} + 6 q^{6} + 6 q^{7} + O(q^{10}) \) \( 378 q + 6 q^{4} + 6 q^{6} + 6 q^{7} + 6 q^{11} - 6 q^{12} - 9 q^{13} - 6 q^{14} - 18 q^{16} + 21 q^{19} + 15 q^{21} + 24 q^{23} - 24 q^{24} - 12 q^{26} - 3 q^{27} - 42 q^{28} + 36 q^{29} + 48 q^{31} + 126 q^{32} + 6 q^{33} + 54 q^{34} + 6 q^{36} - 108 q^{38} + 60 q^{41} - 12 q^{42} - 51 q^{43} + 96 q^{44} + 42 q^{46} + 78 q^{47} - 24 q^{48} - 165 q^{49} + 12 q^{51} - 18 q^{52} - 18 q^{53} + 6 q^{54} - 72 q^{56} + 12 q^{57} + 96 q^{58} + 18 q^{59} - 54 q^{61} - 120 q^{62} + 6 q^{63} - 210 q^{64} + 48 q^{66} - 15 q^{67} + 30 q^{68} + 84 q^{71} - 36 q^{72} - 15 q^{73} - 60 q^{74} + 132 q^{76} - 168 q^{77} + 120 q^{78} + 84 q^{79} - 66 q^{82} + 30 q^{83} + 72 q^{86} - 24 q^{87} - 72 q^{88} - 168 q^{89} - 42 q^{91} - 120 q^{92} - 12 q^{94} + 24 q^{96} - 54 q^{97} - 192 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1425, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1425, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1425, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)